1.1 Quantum Mechanics
1.2 Background
1.3 Postulate I of Quantum Theory
1.4 Vector Spaces
1.5 Hilbert Space
1.6 Function Space
1.7 Postulate II of Quantum Theory
1.8 Linear Operators
1.9 Eigenvalues and Eigenvectors
1.10 Postulate IV of Quantum Theory
1.11 Postulate V of Quantum Theory
1.12 Compatible observables
1.13 Heisenberg Uncertainty Principle
1.14 Alternative Postulates of Quantum Theory
1.15 Postulate III of Quantum Theory
1.16 Time Evolution Operator
1.17 Constants of Motion
1.18 Hamiltonian of a Molecule

2.1 Classical Mechanics
2.2 Reformulations of Classical Equations of Motion
2.3 Energy Formulation of the Equation of Motion
2.4 Lagrange’s Equations of Motion
2.5 Hamilton’s Equations of Motion and the Hamiltonian
2.6 Electrodynamics and Maxwell’s Equations
2.7 Classical Hamiltonian of a Charged Particle Interacting with an Electromagnetic Field
2.8 The Quantum Mechanical Hamiltonian Operator for a Charged Particle in a Field
2.9 The Hamiltonian of a Molecule in an Electromagnetic Field
2.10 Gauge Invariance and the Electromagnetic Wave Equations
2.11 The Hamiltonian of the Free Electromagnetic Field
2.12 Quantum Harmonic Oscillators and the Electromagnetic Field
2.13 The Hamiltonian of a Molecule in an Electromagnetic Field

3.1 Perturbation Theory and Time Evolution of the System
3.2 Transition Probabilities
3.3 Evaluation of the Matrix Elements of the Interaction
3.4 The Long Wavelength Approximation
3.5 The Dipole Approximation
3.6 Absorption Spectroscopy
3.7 Fermi’s Golden Rule
3.8 Two-Photon Absorption Spectroscopy
3.9 Spontaneous Raman Spectroscopy
3.10 Resonance Fluorescence
3.11 The Raman Scattering Tensor

4.1 The Born-Oppenheimer approximation
4.2 Adiabatic Born-Oppenheimer Approximation
4.3 The Crude Born-Oppenheimer Approximation
4.4 The Electronic States
4.5 Vibrational States (Harmonic Oscillator)
4.6 Vibronic Coupling and the Approximate Vibronic States

6.1 Plane Waves
6.2 Wave Packets